Expert: Richard J. Raridon - 4/13/2011

Question
Hi Mr. Richard!

I have an extra credit problem that I would appreciate some help with. Here is the problem:

If the six digits 1, 2, 3, 5, 5, and 8 are randomy arranged into a six digit positive integer, what is the probability that the integer is divisible by 15? Write your answer as a fraction in simplest form.

There ya go! Hope to get a response soon!

Thank you so much,
Timothy

Answer
If a number is divisible by 15 it has to be divisible by 3 and 5.  For a number to
be divisible by 3, the sum of the digits have to add up to a multiple of 3.
Since 1+2+3+5+5+8 = 24, every combination of those numbers is divisible by 3.
For a number to be divisible by 5, the last digit has to be 0 or 5.  In this
case, since there are two 5's, one third of all combinations will have a
5 for the last digit.  Therefore, the probability of being divisible by
15 is 1/3